Variational Data Assimilation in Chaotic Regime by Lorenz Model

Abstract

This paper explores some aspects of data assimilation by 3D-Var method implemented in the Lorenz model. This system was chosen because, although simple, has similar structure to the atmosphere under certain parameters. Conceptual models allow difficult judgments to be made in primitive equation models with their various nonlinear interactions at various scales. It is shown the need to apply data assimilation techniques in highly sensitive models to initial conditions. It was also shown that 3D-Var method is very dependent on the number of cycles during the process of minimizing of the cost function. In the experiment performed on this work was found that at least 1,000 interactions are necessary to solve this minimization problem. However the technique fail to 40% noise added to initial conditions, comparing to control. Additional experiments show the difficulty of performing high quality data assimilation in chaotic dynamics for underdetermined systems, such as the Earth's atmosphere.